Question

Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 175 people. The sample mean is 23.8 hours. There is a known population standard deviation of 6.2 hours. The population distribution is assumed to be normal.

1. Find the following:

1. The sample mean x
2. The population standard deviation σ
3. The sample size n

2. Let X be the time needed to complete one person's tax forms, and X the mean time needed to complete tax forms from a sample of 175 customers.

Note that before the sample is drawn X is a normal random variable but after the sample is drawn x is an actual number. What distribution for X

should you use for this problem? (Give the distribution family of X , the mean of X , and the standard deviation of X ).

3. Construct a 90% conf interval for the mean time to complete the tax forms.
4. If the firm did another survey, kept the error bound the same, and only surveyed 49 people, what would happen to the level of confidence? Why?. Pick one of the following:

1. The level of confidence would be smaller because we have collected a smaller sample, obtaining less accurate information.
2. The level of confidence would be larger because we have collected a smaller sample, obtaining less accurate information.

iii. There would be no change.

Answer 1